Lagrangian finite‐element analysis of time‐dependent viscous free‐surface flow using an automatic remeshing technique: Application to metal casting flow

Abstract

International audienceThe Navier-Stokes incompressible model is used to describe two-dimensional metal casting flow. Such flows involve moving free boundaries. A new numerical algorithm has been developed using the Lagrangian finite-element method. It allows treatment of flows with moderate Reynolds numbers. The main feature is to avoid the calculation of the convective term, together with an automatic remeshing technique, to cure the mesh distortions. The problem of the free oscillation of a liquid is treated to verify the formulation. An application of this method to the computation of an industrial metal casting flow situation is presented

An Eulerian Finite Element Method for Time-Dependent Free Surface Problems in Hydrodynamics

“…First the velocity at time tn+' is estimated by fJ'+' = AtM-' HI"' + q , (12) which is obtained by replacing Pn+' with P" in equation (10). Since the velocity thus calculated does not necessarily satisfy equation (9), it is labelled by a tilde.…”

Velocity-Based Moving Mesh Methods for Nonlinear Partial Differential Equations

“…The most common approach has been through discretizations of the Eulerian description where the equations of motion are discretized on a fixed mesh. Use of the Lagrangian description has been rarer and largely confined to problems where surfaces and interfaces are of primary importance, e.g., [108,118,147]. The natural discretization in the Lagrangian approach is to follow the velocities of the fluid particles using a moving mesh but compromises have usually had to be made, the main difficulty being the tendency of the mesh to tangle and lose its character.…”

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